Alright then! Before we begin let us brainstorm some ideas here. I have a couple for the setting of the story.
The first idea is based on Lost in Space. Our characters are marooned on a desolate planet, forced to survive by our wits and fortitude. We arrived on a small interstellar ship that was malfunctioning and just barely managed to crash-land. We know very little about this planet, except that it is alien and bizarre.
The other idea I have is based on Firefly. Our characters own (or stole) a space ship and we exist on the fringes of galactic civilization, smuggling illicit goods and going places no one else wants to go in order to survive. We aren't necessarily pirates, but we aren't really good guys either. Han Solo and Chewbacca might be a good example of this kind of space ruffian. Trying to eke out an existence on the edges of known space, our characters tend to encounter new and exotic things rather often.
Or we could put our heads together and try to come up with something even more novel. Something that is kind of percolating in my mind right now is a universe, perhaps far future Earth, where a very tiny minority of people have evolved the ability to warp space and time using thought alone, allowing them to travel near infinite distances in the blink of an eye, stop time, and in some cases even alter time. Such powers come at a cost however. All such individuals are ruthlessly hunted down and therefore forced to conceal their true nature. Nevertheless there are some who use this ability to try and work good in the universe, and there are also those who attempt to exploit it for their own personal gain.
I am sure there are other ideas too. Feel free to suggest something!